Your approach is fine; however I don't think your determinant computation is correct. You've set it up properly, but I get just
for the determinant.
Hi there. Well, I have some doubts about this exercise, I think I've solved it, but I wanted your opinion, which always help. So, it says:
There is no general method for solving the homogeneous general equation of second order
But if we already know a solution , then we always can find a second solution linearly independent
Demonstrate that this functions form a basis for the space of solutions of the differential equation (1).
So, what I did is simple. I know that if the solution is linearly independent, then the Wronskian must be zero. So, I just made the calculus for the wronskian:
Is this right?
This is pretty much like the same. It gives me a differential equation, and one solution and asks me for the entire solution. Did I do it well?
Is that okey? I'm not sure, because I've tried to corroborate the solution with wolfram alpha, but it gives something different.
(1-2x)y''+2y'+(2x-3)y=0 - Wolfram|Alpha